Appreciations and Overvaluations
Macroeconomics IV
Ricardo J.
Caballero
MIT
Spring 2011
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 1 / 54

Introduction
Real exchange rate appreciations often refiect boom conditions, but they also stress important parts of the economy
Most economies experience episodes of this sort.
Today, this is the case of commodity producing economies, emerging markets, as well as countries experiencing strong capital infiows
In this context the question arises whether there is a need for policy intervention
Here we present one framework to address such question
(Caballero-Lorenzoni)
Spring 2011 2 / 54 R.J.
Caballero (MIT)
Appreciations and Overvaluations

Motivation: Appreciations
Episodes of large and persistent appreciations of real exchange rate
Many sources:
Absorption of large capital infiows
Infiation stabilization policies
Exchange rate adjustments in trading partners
Favorable price shock for commodity producers
Discovery of natural resources (Dutch disease)
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 3 / 54

Slow adjustment in recoveries
Persistent appreciations drains resources of export sector, lead to destruction/bankruptcies
May slow down export sector recovery once things turn around
Depressed input demand from consumers + depressed input demand from export sector
Real exchange rate overshooting
Spring 2011 4 / 54 R.J.
Caballero (MIT)
Appreciations and Overvaluations

RER overshooting
R.J.
Caballero (MIT)
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Policy question
Is there a need to intervene to protect the export sector?
Does costly ex post adjustment justify intervention ex ante?
A: no
Add extra ingredient: financial constraint
A: in some cases
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 6 / 54

Inter-temporal pecuniary externality
Suppose consumers reduce their demand for non-tradables in appreciation
Less destruction ex-ante and a faster recovery ex-post
Higher wages and real exchange rates ex post
Rational atomistic consumers ignore this effect
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 7 / 54

Related work
’Dutch disease’(Corden, Krugman, Wijnbergen) learning-by-doing, real externality
Broader problem: preventive measures during appreciations and current account deficits ineffi cient current account deficits (Blanchard)
Financial development and the negative effects of macro volatility exchange rate fiuctuations bad for liquidity constrained entrepreneurs
(Aghion-Bacchetta-Ranciere-Rogoff, Aghion-Angeletos-Banerjee-Manova)
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 8 / 54

Model two goods: tradable T , non-tradable N price of N (RER): p t two countries: home, foreign two groups in home country: consumers, entrepreneurs
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 9 / 54

Preferences
Consumers:
Entrepreneurs and ROW:
E
∑
β t
θ t
� log c t
T
+ log c t
N
� preference shock
θ t
E
∑
β t c t
T
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 10 / 54

Shocks
First shift to
θ A
, then shift to
θ D w.p.
δ
θ A
>
θ D
D absorbing state complete markets
R.J.
Caballero (MIT)
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Spring 2011 11 / 54

Endowments
Consumers sell 1 unit of labor inelastically
Entrepreneurs, period 0: a
0 tradable goods n
− 1 production units
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Caballero (MIT)
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Spring 2011 12 / 54

Technology
Tradable sector f of tradable good to create one production unit
( Leontief ) 1 production unit produces 1 tradable using 1 labor
( No mothballing ) if production unit inactive → destroyed
Non-tradable sector
1 unit of labor produces 1 unit of NT
→ wages are equal to p t
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Caballero (MIT)
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Financial constraint
No commitment on entrepreneurs’side
Portfolio of entrepreneurs: a ( s t + 1
| s t
) ≥ 0
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Caballero (MIT)
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Equilibrium: consumers
Consumers’optimality + complete markets
Demand for NT c
N t
=
κ
θ t p t shock: persistent shift in demand for NT
κ endogenous depends on NPV of wages p t
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Caballero (MIT)
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Equilibrium: export units and NT consumption
Market clearing in labor and goods market + Leontief: n t
+ c t
N
= 1
Market clearing for used units + creation/destruction margin: q t n t n t
∈ [ 0 , f ]
> n t − 1
< n t − 1 implies q t
= f implies q t
= 0 q t price of used unit
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Caballero (MIT)
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Characterization
Proposition
Equilibrium is characterized by:
Phase A p ( s t
) = p
A
> 1 q ( s t
) = 0
Phase D p ( s t
) = p
D , j
< 1 q ( s t
) = f
D , j : j-th period after reversal
Assumptions:
θ A
/
θ D and n
− 1 suffi ciently large
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Caballero (MIT)
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First Best — Phase A : Operational losses and option value
Cost of holding a unit:
Expected benefit: p
A
− 1 > 0
βδ f
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Caballero (MIT)
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Phase D : Recovery
Cost of holding a unit: f − ( 1 − p
D , j
) > 0
Expected benefit:
β f
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Caballero (MIT)
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First best (large a
0
)
Price pinned down by intertemporal margin on the supply side
Indifference between financial assets and physical capital p fb
A
− 1 =
βδ f f + p fb
D
− 1 =
β f
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Caballero (MIT)
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First best
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Caballero (MIT)
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First best
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Caballero (MIT)
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First best (continued)
Cutoff a fb
If a
0
≥ a fb financial constraint not binding
High wealth a
0 needed for two reasons: cover losses in A cover investment costs in first period of D
( p
A
− 1 ) n
A
+
δβ a
D , 0
= ( 1 − ( 1 −
δ
)
β
) a
0
R.J.
Caballero (MIT)
Appreciations and Overvaluations
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Constrained equilibrium: Low a
0
Prices no longer pinned down by intertemporal margin
Limited ability to exchange financial assets for physical capital p
A
− 1 ≤
βδ f f + p
D , j
− 1 ≤
β f
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Caballero (MIT)
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Entrepreneur’s problem: recursive setup
Equilibrium prices taken as given: q ( s t
) and p ( s t
)
Individual state variables: financial wealth a physical capital n
−
Lemma
The value function V ( a , n
−
; s t
) takes the linear form
V
� a , n
−
; s t
�
=
ψ
( s t
) +
φ
( s t
)
� a + q ( s t
) n
−
�
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 25 / 54

Bellman equation
φ
� s t
� � a + q
� s t
� n
−
�
=
= max c c T , e , n , a ( .
)
T , e
+
β
E
�
φ
( s t + 1
)
� a ( s t + 1
) + q ( s t + 1
) n
�� s .
t .
c
T , e
+ q ( s t
) · n +
β
E [ a ( s t + 1
)] = ( 1 − p ( s t
)) · n + a + q ( s t
) · n
− a ( s t + 1
) ≥ 0 , n ≥ 0 , c
T , e
≥ 0
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 26 / 54

Optimality conditions
For physical capital (production units):
�
( ) + p ( s t
) − 1
�
=
β
E
�
φ
� s
φ
( t + 1
� s t ) q
� s t + 1
�
�
For securities:
φ
� s t
�
≥
φ
� s t + 1
� a
� s t + 1
| s t
�
≥ 0
For consumption:
1 ≤
φ
� s t
� c
T , e
� s t
�
≥ 0
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 27 / 54

Low a
0
Limited funds a
0
( p
A
− 1 ) n
A
+
δβ a
D , 0
= ( 1 − ( 1 −
δ
)
β
) a
0 keep resources for A insure the recovery
Low a
0 can bite in A , in D , both...
R.J.
Caballero (MIT)
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Spring 2011 28 / 54

Constrained appreciation
Units only pay back in state D
( p
A
− 1 )
φ
A
φ
A
=
βδ f
φ
D , 0
≥
φ
D , 0
If constraint is binding then p
A
− 1 <
βδ f
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 29 / 54

Constrained appreciation (continued)
Proposition
If a
0
< a
A then price is depressed p
A
< p fb
A
, destruction is bigger n
A
< n fb
A
Smaller appreciation, symptom of financial distress
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 30 / 54

Constrained appreciation (continued)
R.J.
Caballero (MIT)
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Overshooting
Proposition
If a
0
< a
D then overshooting: p
D , 0
< p fb
D p
D , j
→ p fb
D constrained recovery f + p
D , 0
− 1 <
β f
→ low wages help recovery of financially constrained firms
R.J.
Caballero (MIT)
Appreciations and Overvaluations
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Overshooting (continued)
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Caballero (MIT)
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Constrained equilibrium
R.J.
Caballero (MIT)
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General equilibrium feedback
Back to consumers’demand
κ
=
E ∑
β t p t
2 E ∑ t
β θ t
Now
κ depends on initial wealth of entrepreneurs
R.J.
Caballero (MIT)
Appreciations and Overvaluations
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R.J.
Caballero (MIT)
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Exchange rate policy
Exchange rate appreciation in A leads to
→ more destruction in A
→ slower recovery in D
Policy: Relieve pressure on demand for NT, increase n
A
, save units for the recovery
Q: Is this policy welfare improving?
R.J.
Caballero (MIT)
Appreciations and Overvaluations
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Policy instruments no transfers between consumers and entrepreneurs taxes on consumption of T/NT, rebated lump-sum to consumers interventions with effects in this direction: contractionary fiscal policy policies to encourage savings currency interventions/reserves management (?)
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 38 / 54

Planner problem
Planner chooses: state contingent path for c
T
( s t
) , c
N
( s t
)
Takes as given: market clearing in labor market n ( s t
) = 1 − c
N
( s t
) entrepreneurs’optimality
Map n ( .
) → p ( .
) , a ( .
) , c
T , e
( .
) maximize consumers’utility for fixed entrepreneurs’utility
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 39 / 54

Perturbation
Increase n
A locally, around CE
Effects on consumers’welfare (leaving entrepreneurs indifferent)
Result If constrained appreciation and overshooting then: dU c
> 0 dU e
= 0
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 40 / 54

Perturbation (continued)
Change n
A locally, around CE dU c dn
A
= −
θ A u
�
( 1 − n
A
) + p
A λ
+
+
λ
�
∂ p
∂ n
A n
A
A
+
βδ
∂ p
D , 0
∂ n
A n
D , 0
�
λ lagrange multiplier on consumers BC first row zero (private FOC)
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 41 / 54

Ineffi cient destruction
If constrained appreciation + overshooting ( p
A
< p fb
A and p
D , 0
< p fb
D
) then
∂ p
A
∂ n
A n
A
+
δβ
∂ p
D , 0
∂ n
A n
D , 0
= 1 − p
A
+
βδ f > 0 total wage loss today = cost of saving an extra unit total wage gain tomorrow = savings in investment costs
Spring 2011 42 / 54 R.J.
Caballero (MIT)
Appreciations and Overvaluations

Ineffi cient destruction (continued)
If p
D , 0
< p fb
D
(overshooting) then: dU e dn
A
=
∂ c
T , e
D , 0
∂ n
A
= 0 all extra funds tomorrow go to investment
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 43 / 54

Constrained effi ciency
If no overshooting optimal policy is no intervention
∂ p
A
∂ n
A n
A
+
δβ
∂ p
D , 0
∂ n
A n
D , 0
= 1 − p
A
< 0 only wage losses today then reduce n
A
?
no, the entrepreneur PC binding now
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 44 / 54

Optimal policy
Optimal policy if no constrained appreciation?
Intervention during recovery phase still good
In general optimal to combine intervention in A and D
Hindrances: real wage rigidities in recovery nominal wage rigidities + peg
R.J.
Caballero (MIT)
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Optimal policy (continued) blue - CE, red - optimal policy
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Caballero (MIT)
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Ex ante vs ex post: Three cases
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Three cases (continued)
First case, low a
0 intervention in A is very effective tax NT in A and subsidy in D subsidy eventually vanishes
Second case, middle a
0 intervention in A is effective but also leave some for D a ll intervention in D frontloaded
Third case, high a
0 intervention more effective in D over-overshooting
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Caballero (MIT)
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a
0 and intervention (against CE)
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Implementation: tax on nontradable
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Caballero (MIT)
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Persistence
How does
δ affect the equilibrium, the incentive to intervene?
High
δ
: switch is very likely small losses, easy to hedge
Low
δ
: switch is very unlikely optimal to destroy many units also in first best, easy to hedge
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 51 / 54

Persistence (continued) shaded region - positive taxes
R.J.
Caballero (MIT)
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Incomplete markets
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Caballero (MIT)
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Conclusions
Appreciation can generate excessive destruction
For ineffi ciency, it is crucial that there is a constrained recovery
Trade-off wage cut in A v.
faster recovery in D
Menu of intervention depends on initial conditions: more constrained entrepreneurs, more preventive policy
R.J.
Caballero (MIT)
Appreciations and Overvaluations
Spring 2011 54 / 54

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Spring 2011
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